Search for: All records

Abstract Pertaining to the motion of a rigid particle in a flow, several distinct “centers” of the rigid particle can be identified, including the geometric center (centroid), center of mass, hydrodynamic center, and center of diffusion. In this work, we elucidate the relevance of these centers in Brownian motion and diffusion. Starting from the microscopic stochastic equations of motions, we systematically derive the coarse-grained Fokker–Planck equations that govern the evolution of the probability distribution function (PDF) in phase space and in configurational space. For consistency with the equilibrium statistical mechanics, we determine the unknown Brownian forces and torques. Next, we analyze the Fokker–Planck equation for the PDF in the position and orientation space. Through a multiscale analysis, we find the unit cell problem for defining the effective long-time translational diffusivity of a particle of arbitrary shape in an external orienting field. We also show some fundamental properties of the effective long-time translational diffusivity, including rigorous variational bounds for effective long-time diffusivity and invariance of effective diffusivity with respect to change of reference or tracking points. Exact results are obtained in the absence of an orienting field and in the presence of a strong orienting field. These fundamental results hold significant potential for applications in biophysics, colloidal science, and micro-swimmers design. 

Abstract BackgroundInhomogeneous patterns of chromatin-chromatin contacts within 10–100-kb-sized regions of the genome are a generic feature of chromatin spatial organization. These features, termed topologically associating domains (TADs), have led to the loop extrusion factor (LEF) model. Currently, our ability to model TADs relies on the observation that in vertebrates TAD boundaries are correlated with DNA sequences that bind CTCF, which therefore is inferred to block loop extrusion. However, although TADs feature prominently in their Hi-C maps, non-vertebrate eukaryotes either do not express CTCF or show few TAD boundaries that correlate with CTCF sites. In all of these organisms, the counterparts of CTCF remain unknown, frustrating comparisons between Hi-C data and simulations. ResultsTo extend the LEF model across the tree of life, here, we propose theconserved-current loop extrusion (CCLE) modelthat interprets loop-extruding cohesin as a nearly conserved probability current. From cohesin ChIP-seq data alone, we derive a position-dependent loop extrusion rate, allowing for a modified paradigm for loop extrusion, that goes beyond solely localized barriers to also include loop extrusion rates that vary continuously. We show that CCLE accurately predicts the TAD-scale Hi-C maps of interphaseSchizosaccharomyces pombe, as well as those of meiotic and mitoticSaccharomyces cerevisiae, demonstrating its utility in organisms lacking CTCF. ConclusionsThe success of CCLE in yeasts suggests that loop extrusion by cohesin is indeed the primary mechanism underlying TADs in these systems. CCLE allows us to obtain loop extrusion parameters such as the LEF density and processivity, which compare well to independent estimates. 

Predictive modeling in physical science and engineering is mostly based on solving certain partial differential equations where the complexity of solutions is dictated by the geometry of the domain. Motivated by the broad applications of explicit solutions for spherical and ellipsoidal domains, in particular, the Eshelby’s solution in elasticity, we propose a generalization of ellipsoidal shapes called polynomial inclusions. A polynomial inclusion (or -inclusion for brevity) of degree is defined as a smooth, connected and bounded body whose Newtonian potential is a polynomial of degree inside the body. From this viewpoint, ellipsoids are identified as the only -inclusions of degree two; many fundamental problems in various physical settings admit simple closed-form solutions for general -inclusions as for ellipsoids. Therefore, we anticipate that -inclusions will be useful for applications including predictive materials models, optimal designs, and inverse problems. However, the existence of p-inclusions beyond degree two is not obvious, not to mention their explicit algebraic parameterizations. In this work, we explore alternative definitions and properties of p-inclusions in the context of potential theory. Based on the theory of variational inequalities, we show that -inclusions do exist for certain polynomials, though a complete characterization remains open. We reformulate the determination of surfaces of -inclusions as nonlocal geometric flows which are convenient for numerical simulations and studying geometric properties of -inclusions. In two dimensions, by the method of conformal mapping we find an explicit algebraic parameterization of p-inclusions. We also propose a few open problems whose solution will deepen our understanding of relations between domain geometry, Newtonian potentials, and solutions to general partial differential equations. We conclude by presenting examples of applications of -inclusions in the context of Eshelby inclusion problems and magnet designs. 

The chromosomes—DNA polymers and their binding proteins—are compacted into a spatially organized, yet dynamic, three-dimensional structure. Recent genome-wide chromatin conformation capture experiments reveal a hierarchical organization of the DNA structure that is imposed, at least in part, by looping interactions arising from the activity of loop extrusion factors. The dynamics of chromatin reflects the response of the polymer to a combination of thermal fluctuations and active processes. However, how chromosome structure and enzymes acting on chromatin together define its dynamics remains poorly understood. To gain insight into the structure-dynamics relationship of chromatin, we combine high-precision microscopy in living Schizosaccharomyces pombe cells with systematic genetic perturbations and Rouse model polymer simulations. We first investigated how the activity of two loop extrusion factors, the cohesin and condensin complexes, influences chromatin dynamics. We observed that deactivating cohesin, or to a lesser extent condensin, increased chromatin mobility, suggesting that loop extrusion constrains rather than agitates chromatin motion. Our corresponding simulations reveal that the introduction of loops is sufficient to explain the constraining activity of loop extrusion factors, highlighting that the conformation adopted by the polymer plays a key role in defining its dynamics. Moreover, we find that the number of loops or residence times of loop extrusion factors influence the dynamic behavior of the chromatin polymer. Last, we observe that the activity of the INO80 chromatin remodeler, but not the SWI/SNF or RSC complexes, is critical for ATP-dependent chromatin mobility in fission yeast. Taking the data together, we suggest that thermal and INO80-dependent activities exert forces that drive chromatin fluctuations, which are constrained by the organization of the chromosome into loops. 

Solution-printable and flexible thermoelectric materials have attracted great attention because of their scalable processability and great potential for powering flexible electronics, but it is challenging to integrate mechanical flexibility, solution-printability and outstanding thermoelectric properties together. In particular, such an n-type thermoelectric material is highly sought after. In this paper, 2D TiS 2 nanosheets were exfoliated from layered polycrystalline powders, and then assembled with C 60 nanoparticles, resulting in a new class of flexible n-type thermoelectric materials via a concurrent enhancement in the power factor and a reduction in thermal conductivity. The resultant C 60 /TiS 2 hybrid films show a ZT ∼ 0.3 at 400 K, far superior to the state-of-the-art solution-printable and flexible n-type thermoelectric materials. In particular, such a thermoelectric property rivals that of single-crystal TiS 2 -based thermoelectric materials, which are expensive, difficult to synthesize, and unsuitable for solution printing. A solution of the C 60 /TiS 2 hybrid was also used as an ink for printing large-area flexible and spatial thermoelectric devices. An outstanding output power of 1.68 W m −2 was generated at a temperature gradient of 20 K. This work paves the way for flexible, solution-printable, high-performance thermoelectric materials for flexible electronics.